# Thread: L'Hospital's rule with trigs

1. ## L'Hospital's rule with trigs

Hello all!

I need some help with this question:

the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

so lim as x-> 0 of the xth root of $(sinx+cosx)$

is that right?

2. ## Re: L'Hospital's rule with trigs

Originally Posted by kingsolomonsgrave
Hello all!

I need some help with this question:

the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

so lim as x-> 0 of the xth root of $(sinx+cosx)$

is that right?
if
$y=\lim_{x->0}[cos(x)+sin(x)]^{1/x}$

so: $ln(y)=\lim_{x->0}ln[[cos(x)+sin(x)]^{1/x}]$
Now you most use the logarithmic power rule and you will get indeterminate form: 0/0

3. ## Re: L'Hospital's rule with trigs

$ln(y)=$lim as x->0 $ln(sinx/x + cosx/x)$
am I on the right track?

4. ## Re: L'Hospital's rule with trigs

Originally Posted by kingsolomonsgrave
$ln(y)=$lim as x->0 $ln(sinx/x + cosx/x)$
am I on the right track?
This is not true you cant bring the $\frac{1}{x}$ "into" your ln function. You want to write $\frac{\ln( \sin(x) + \cos(x))}{x}$